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The president imitates McConnell by slumping his shoulders and looking lethargic, and emulates the dramatic thumbs down McCain used to indicate his "no" vote on the GOP healthcare bill in July.
Trump has repeatedly lashed out both at McConnell and McCain, most recently over Congress's failure to pass legislation repealing and the Affordable Care Act.
The president called McCain's recent opposition to the latest incarnation of the GOP healthcare bill a "tremendous slap in the face to the Republican Party," and placed full blame for legislative failure on McCain.
"You can call it what you want, but that's the only reason we don't have it, because of John McCain," Trump said in a radio interview on Monday.
Trump has also repeatedly expressed his frustration with McCain on Twitter. On Monday, the president tweeted a six minute-long video montage of the senator and former presidential candidate publicly promising to get rid of Obamacare.
McConnell, another repeat Trump target, drew continued criticism from the president for his inability to deliver on the longstanding GOP promise. During the Monday radio interview, Trump brought up the majority leader's low approval rating with constituents.
"Mitch is not, polling-wise, the most popular guy in this country," Trump said.
Trump has also placed blame on McConnell's shoulders for Republican candidate Luther Strange's loss in Alabama's Senate primary to Roy Moore, an anti-establishment candidate who was backed by some of Trump's most fervent supporters.
Bob Bryan contributed to this report.